Image denoising using bivariate alpha-stable distributions in the complex wavelet domain

Recently, the dual-tree complex wavelet transform has been proposed as a novel analysis tool featuring near shift-invariance and improved directional selectivity compared to the standard wavelet transform. Within this framework, we describe a novel technique for removing noise from digital images. We design a bivariate maximum a posteriori (MAP) estimator, which relies on the family of isotropic alpha-stable distributions. Using this relatively new statistical model we are able to better capture the heavy-tailed nature of the data as well as the interscale dependencies of wavelet coefficients. We test our algorithm for the Cauchy case, in comparison with several recently published methods. The simulation results show that our proposed technique achieves state-of-the-art performance in terms of root mean squared error.